I think that Caris with pronunciation cah-ris works better than with pronunciation kerri-is. If you introduce yourself as Caroline with nn Caris, I think it works perfectly. Nicknames don't have to be completely derived from your given name - I think they work best when they do make a nod to it however, which is was Caroline nn Caris does.

Anyway. I don't think it works with the 'care-iss' pronunciation as there's no 'care' sound in Caroline. You'd have to say it 'KAH-riss', the way Carys is traditionally pronounced, for it to make sense.